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August  2013, 6(4): 1017-1027. doi: 10.3934/dcdss.2013.6.1017

On a structure of the fixed point set of homogeneous maps

Yakov Krasnov 1,2,3, , Alexander Kononovich 1,2,3, and  Grigory Osharovich 1,2,3,

1. 

Department of Mathematics
2. 

Bar-Ilan University
3. 

Ramat-Gan, 52900

Received  June 2011 Revised  September 2011 Published  December 2012

A spectral and inverse spectral problem for homogeneous polynomial maps is discussed.The $m$-independence of vectors based on the symmetric tensor powers performs as a main toolto study the structure of the spectrum. Possible restrictions on this structureare described in terms of syzygies provided by the Euler-Jacobi formula.Applications to projective dynamics are discussed.
Keywords: Fixed points theory, Bzout theorem, Euler-Jacobi formula, multi-linear analysis, syzygies..
Mathematics Subject Classification: Primary: 34A34, 15A69; Secondary: 15A18, 34C14, 34C4.
Citation: Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017
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show all references

References:
[1]

Bull. London Math. Soc., 13 (1981), 412-414. doi: 10.1112/blms/13.5.412.  Google Scholar

[2]

Ann. of Math. (2), 88 (1968), 451-491.  Google Scholar

[3]

Comm. Algebra, 31 (2003), 4571-4609. doi: 10.1081/AGB-120022810.  Google Scholar

[4]

"Proc. Edinburgh Math. Soc." (2), 55, Issue 3, (2012), 577-589. Google Scholar

[5]

Berlin, New York: Springer-Verlag, 1974.  Google Scholar

[6]

Bull. London Math. Soc., 36 (2004), 378-382. doi: 10.1112/S0024609303002820.  Google Scholar

[7]

Second edition, in "Ergebnisse der Mathematik und ihrer Grenzgebiete," Springer-Verlag, 2 1998. doi: 10.1007/978-1-4612-1700-8.  Google Scholar

[8]

Acta Sci. Math. (Szeged), 39 (1977), 341-351.  Google Scholar

[9]

J. Dyn. Diff. Equat., 21 (2009), 487-499. doi: 10.1007/s10884-009-9141-x.  Google Scholar

[10]

Berlin, New York: Springer-Verlag, Band 213, 1974.  Google Scholar

[11]

J. Amer. Math. Soc., 6 (1993), 459-501. doi: 10.2307/2152805.  Google Scholar

[12]

Topological Methods in Nonlinear Analysis, 19 (2002), 257-273.  Google Scholar

[13]

Ann. Math., 66 (1957), 545-556.  Google Scholar

[14]

Bull. London Math. Soc., 11 (1979), 177-183. doi: 10.1112/blms/11.2.177.  Google Scholar

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